In restorative dentistry, tooth shapes are typically generated based on a small set of sample tooth shapes called library teeth. Such library teeth are stored in tooth libraries and manipulated using 3D digital editing techniques that are equivalent to the physical processes of sculpting in wax and clay (i.e., by adding or removing material digitally from areas on the surface of the model in a manner analogous with adding or removing wax in physical modeling). This allows for a wide variation, but provides no means for assuring that the result continues to be a natural tooth shape. In particular, this approach has three primary problems:                1. It is a time consuming process.        2. It requires full dental knowledge and artistic skill to create a dentally appropriate tooth shape.        3. It does not prevent the result from not being an appropriate anatomical shape, should the knowledge and skill not be complete.        
Other approaches for modeling natural tooth shape have been contemplated. First, one could create a completely parametric model of teeth. Unfortunately, a huge amount of parameters would be needed to correctly define a tooth. Even with such a model, it would be necessary to “imprint” fine detail onto the resulting parametric model. In any case, the model would be too time-consuming to use to design a specific tooth. On the other hand, a library of teeth could be morphed to create crown shapes. Those libraries naturally have the detail, but the libraries do not offer a way to automate the structurally important details. In a further approach, post processing of a statistical tooth model could be used to “imprint” a tooth-like pattern on the various regions of the final tooth shape. Unfortunately, such an approach results in a model that may have edge artifacts between the regions. Also, this process is computationally complex and error prone.
Other techniques are known in the art for generating a statistical tooth model using mathematical techniques known as principal component analysis (PCA). For example, U.S. Pat. No. 8,727,776 to Mehl discloses a method for producing denture parts or tooth restorations using electronic dental representation generating using PCA. PCA reduces the complexity of modeling an anatomical shape by looking at the characteristics of a set of samples and defining those elements of the sample that best characterize differences across the samples. A similar approach is described by Gurke in “Generating geometrically deformable models by statistical shape modeling for computer aided dental restorations,” CARS 2000, Lemke, et al. editors (2000), which describes development of a tooth model based on a form of statistical shape analysis known as the Point Distribution Model including an analysis of the shape variance of a training set using eigenvectors and the definition of significant dental medical features. The weighted amounts of each eigenvector are added to the mean tooth shape of the training set to define the tooth model. The tooth model is used in an automatic CAD system for dental restorations. C. Lorenz, et al. also described in an article entitled “Generation of point based 3D statistical shape models for anatomical objects,” Computer Vision and Image Understanding, Vol. 77, Issue 2, pages 175-191, February 2000, a technique for the generation of a statistical shape model for medical objects using PCA where a template shape is developed and all objects to be analyzed are fitted to the template. One of the benefits of these approaches is the processing speed improvements that can be gained by ignoring those aspects of the samples whose variation is not important in distinguishing the resulting tooth model. However, by ignoring these aspects for performance purposes, the resulting model appears less sharp than expected. A technique that provides improved sharpness is desired.
In any of these approaches, the results of creating a statistical model of anatomy can appear to be lacking detail. While the resulting model is structurally complete, customers can be put off by the lack of finished appearance. A technique is desired that delivers an effective statistical model of tooth anatomy while retaining the fine detail that customers expect.
K-means clustering is a known way to partition an N-dimensional data population into k sets on the basis of a sample. The mathematical basis for k-means clustering is described by MacQueen in an article entitled “Some Methods for classification and Analysis of Multivariate Observations,” Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability (1967). Spath also described a technique for k-means clustering in a text entitled “Cluster Dissection and Analysis: Theory, FORTRAN Programs, Examples,” Translated by J. Goldschmidt New York: Halsted Press (1985). Kanungo, et al. also describe in an article entitled “An efficient k-means clustering algorithm: Analysis and implementation,” IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 24, No. 7, pp. 881-892 (July, 2002), an implementation of k-means clustering using Lloyd's algorithm to determine the sample points in a data distribution.
Other approaches for partitioning data are known in the art. For example, Jones et al. describe in “Multidimensional Morphable Models: A Framework for Representing and Matching Object Classes,” International Journal of Computer Vision, Volume 29, Issue 2, pp. 107-131 (1998), a multidimensional morphable model including a stochastic gradient descent algorithm that automatically matches a model to an image for use in computer vision. Blanz et al. similarly describe in an article entitled “A morphable model for the synthesis of 3D faces,” Proceedings of SIGGRAPH 99, pages 187-194, August 1999, a technique for modeling textured 3D faces using a morphable face model by transforming the shape and texture of the examples in to a vector space representation.
It is desirable to create a digital model of teeth by creating a robust model of dental anatomy and then providing techniques for processing such a computationally large model using suitable mathematical processing techniques that allow the model to be processed in a reasonable amount of time without losing necessary detail. The invention addresses these and other needs in the art.